By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N-soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.

Exact solutions of the Hirota equation and vortex filaments motion

DEMONTIS, FRANCESCO;VAN DER MEE, CORNELIS VICTOR MARIA
2015-01-01

Abstract

By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N-soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.
2015
Inverse Scattering Transform; Soliton solutions; Vortex filaments; Statistical and nonlinear physics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/134373
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